Macromolecules 1986, 19, 1013-1021
1013
Semiquantitative Relationship between Polymer Side-Chain Dynamics and Solvent Solubility Pardmeters. Variable-Frequency I3C NMR Relaxation Study of Poly(n-butyl methacrylate) George C. Levy* and Dehua Wangt NIH Research Resource for Multi-Nuclei NMR and Data Processing, Chemistry Department, Syracuse University, Syracuse, New York 13210. Received May 2, 1985
ABSTRACT: Extensive 13C NMR relaxation measurements on poly(n-butyl methacrylate) (PBMA) obtained at three widely separated frequencies (90.6,37.8,and 20.0 MHz) show wide variation of spin-lattice relaxation times (T,s) and nuclear Overhauser effects (NOEs) for the polymer side-chain carbons as a function of the solvent solubility parameter (As). A semiquantitative relationship between polymer side-chain motion and the solubility parameters (and therefore cohesive energy) was established. Several sets of spin-lattice relaxation data from the literature have been rationalized by this relationship. The diamond-lattice conformational jump model (VJGMmodel) has been modified to explain both backbone motion and side-chainmultiple internal rotations. The modified model predicts both correlation times for backbone motion and side-chain multiple internal rotations, which can quantitatively reproduce most of the observed data. A heteronuclear 2D NOE (HOESY) experiment was performed to detect dipolar interactions between the quaternary carbon (C-CR4) and nearby protons. It is found that the NOEs of C-CR4mainly come from dipolar interactions with protons of the attached methyl group C-CH,.
Introduction 13Cdipole-dipole spin-lattice relaxation measurements represent a powerful method for investigating dynamics of molecular motion in polymers. Measurements of 13C spin-lattice relaxation times (Tis), and nuclear Overhauser effects (NOEs) have provided information about backbone motion and segmental internal rotation in synthetic polymers.'-" It has been found in several polymers that T1values of the backbone chain are unaffected by large changes in macroscopic viscosity from varying molecular weight or concentration in the same ~ o l v e n t .However, ~ the T1 values do vary with solvent. Heatley and Wood6 reported the CHp proton Tls for polystyrene in four different solvents. They found that spin-lattice relaxation times in poor solvents were smaller than in good solvents. This implies that segmental motion is hindered in the more tightly coiled conformation adopted in a poor solvent. Similar solvent dependence for main-chain motion has been reported by several other investigator^.^-" However, little information has been obtained about the dependence of side-chain motion on different solvents, especially in concentrated solutions. Poly(n-butyl methacrylate) (PBMA) possesses four protonated carbons in its regular side chain. C-CHJ
C' HJ
,C-CHz
I
I
0 I
I CHZ-CH~-CH~-CH~ 1
2
3
4
We previously reported an extensive 13CNMR relaxation study of this polymer a t a number of temperatures and a t two widely different magnetic field^.^ As a further investigation to include information about the dependence of relaxation on solvents, we have measured spin-lattice relaxation times and NOEs for PBMA in a number of 'Present address: Changchun Institute of Applied Chemistry, China. 0024-9297/86/2219-1013$01.50/0
solvents a t three dispersed magnetic fields. A number of models have been developed for interpretation of spin relaxation data. The simplest motional model is rigid isotropic tumbling, characterized by a single correlation time.12 This model is understandably unable to account for experimental relaxation data for polymer^.^ A second kind of model describes empirical distributions of correlation times. Although C~le-Cole'~and FuossKirkwood14 symmetrical distributions have been used to explain polymer magnetic relaxation, Schaefer's asymmetrical log x2 di~tribution'~ is more proficient. These models have been shown to be consistent with experimental data for many polymers in dilute s o l ~ t i o n . ~ s ~ J ~ However, the physical insight of the empirical distribution models has been q ~ e s t i o n e dsince , ~ there is lack of direct connection with specific polymer motions. The most successful descriptive method to dste combines a crankshaft motion and a three-bond jump on a diamond lattice. This latter model was first derived by Valeur, Jarry, Geny, and Monnerie (VJGM).'6-'8 The VJGM model, however, only satisfies polymer main-chain motions. It cannot be used to explain side-chain multiple internal rotations. In this paper, a model for polymer motion incorporating side-chain segmental internal rotation will be proposed and applied to the interpretation of 13C spin-lattice relaxation of both main-chain and sidechain carbons in PBMA in concentrated solution.
Experimental Section Poly(n-butyl methacrylate) was purchased from Polyscience, Inc., as a high molecular weight material. Solutions were prepared without further purification using reagent-grade toluene, tetrahydrofuran, acetone, dioxane, aniline, quinoline, 2-propanol, and benzyl alcohol. All samples (476 mg/mL, which is equivalent to 50% (w/w) for PBMA in toluene) were prepared by solute concentration. Natural abundance 13Cspectra were obtained with a quadrature detection-modifiedBruker WM-360, in-house design Mohawk-150, and Varian CFT-20 spectrometers, respectively. Free induction decays were accumulated with 4K/4K data points. A fast inversion recovery (FIRFT) pulse ~equence'~ with 3-s delay time between repetitions was used. A total of 16 T values ranging from 0.001 to 5T1 s was used to obtain a given TI data set. The T I values were obtained by using a three-parameter exponential fit and are estimated to be accurate to &5YO. Nuclear Overhauser enhancement factors (NOEFs) were determined with gated decoupling. Two sets of spectra were obtained alternately with two 1986 American Chemical Society
Macromolecules, Vol. 19, No. 4, 1986
1014 Levy a n d Wang Table I
T ,of P o M n -buts1 methacrylate) Carbons in Different Solvents (476 ma/mL) and Different Magnetic Fields a t Ti, s solvent
i 6 , " (ca1/cm3V
toluene tetrahydrofuran chlorobenzene acetone dioxane aniline quinoline 2-propanol benzyl alcohol average
0.15 0.35 0.75 1.15 1.25 1.55 2.05 2.75 3.35
toluene tetrahydrofuran chlorobenzene acetone dioxane aniline quinoline 2-propanol benzyl alcohol average
0.15 0.35 0.75 1.15 1.25 1.55 2.05 2.75 3.35
toluene tetrahydrofuran chlorobenzene acetone dioxane aniline quinoline 2-propanol benzyl alcohol average
0.15 0.35 0.75 1.15 1.25 1.55 2.05 2.75 3.35
c-1 0.54 0.47 0.43 0.46 0.45 0.29 0.39 0.46
c-2
c-3 90.6 MHz 0.55 1.3 1.2 0.60 0.58 1.4 0.59 1.1 0.54 1.0 0.50 0.90 0.47 0.75 0.48 0.80 0.43 0.75
c-4
C-CH,
C-CH,
C-CR,
2.6 2.7 2.7 2.5 2.3 2.2 2.1 2.2 2.0
0.087 0.086 0.086 0.098 0.074 0.090 0.078 0.089 0.087 0.086
0.20 0.19 0.15 0.21 0.20 0.25 0.18
2.4 2.9 2.4 2.8 2.9
1.9 1.9 1.8 1.7 1.7 1.7 1.7
0.047 0.026 0.027 0.040 0.037 0.032 0.027 0.040 0.045 0.036
0.038 0.032 0.035 0.052 0.051 0.035
0.038 0.039 0.030 0.044 0.031 0.041 0.028 0.041 0.040 0.037
0.038 0.022 0.030 0.030 0.010
0.44 0.21 0.16 0.29 0.21 0.25 0.29 0.28 0.22
0.50 0.58 0.45 0.49 0.31 0.30 0.27 0.32 0.25
37.8 MHz 0.90 0.90 0.65 0.61 0.54 0.60 0.61 0.49
1.4
1.5
0.24 0.091 0.065 0.071 0.092 0.075 0.079 0.10 0.10
0.28 0.27 0.29 0.26 0.23 0.22 0.30 0.22
20.0 MHz 0.62 0.71 0.70 0.67 0.45 0.34 0.30 0.55 0.37
0.084
45 "C
1.5 1.5 1.4 1.5 1.6 1.1 1.1
1.2 1.1
0.23 0.20
3.2 3.5 3.5
1.0 1.3 1.3 0.75 1.0 1.4 1.8 1.4 1.6
0.041
0.022 0.020
0.41 0.40 0.47 0.43 0.42 0.64 0.72 0.46 0.57
0.025
'A6 is the difference of solubility parameters between poly(n-butyl methacrylate) (6 = 8.75 ( c a l / ~ m ~ ) 'and / ~ ) solvent. level continuous wideband decoupling and gated decoupling, with a pulse interval greater than 10 times the longest Tl. NOEF values were calculated from the average of the two data sets and were accurate to better than &15%. A program for our motional model was written in Fortran 77 with a Simplex nonlinear least-squares optimization algorithm. The calculations for other models were done with our recently developed program M O L D Y N , ~which enables a scientist to explore over 22 molecular motional models. All the calculations were performed on a Data General MV 8000 minicomputer. T h e pulse sequence for heteronuclear 2D NOE (HOESY) experiments follows:
l a x a t i o n rate l / T 2 ,and the nuclear Overhauser e n h a n c e ment factor were first described b y P u r c e l l and co-work-
'H 9o0-t1/2--t1/2-9O0-t2 l3C
t1/2-180°-t1/2--r,-900
T h e 90' pulse width for 'H was 42 fis. A 16-step phase cycling was used to separate the positive and negative modulation frequencies (hence quadrature detection in Fl),suppress unwanted axial peaks, and cancel the image along Fl = 0. T h e repetition delay was 0.75 s, which is 1.3T1for the mean proton. Because we are interested in dipolar interactions between quaternary carbons and neighboring protons of methyl groups, the mixing time 7, was set a t 0.49 s, which is equal to Tl for the methyl group protons. In order to minimize the required acquisition frequency and amount of data-storage space, as well as to optimize decoupling, the proton transmitter frequencies were set to the center of the chemical shift region of interest. Before Fourier transformation, a Gaussian digital filtering function was applied in Fl and F2 dimensions, respectively. T h e spectrum was obtained on a Bruker WM-360 W B spectrometer equipped with an Aspect2000A computer.
Theory For t w o n o n e q u i v a l e n t s p i n 'Iz nuclei the e x p r e s s i o n s of the spin-lattice relaxation r a t e l/Tl, the spin-spin re-
(3)
where r in this case is the carbon-hydrogen internuclear distance, yI and ys are the magnetogyric ratios of c a r b o n and h y d r o g e n , respectively, N is t h e number of directly a t t a c h e d hydrogens (for l3C--lHd i p o l a r relaxation), Ji(o) is the spectral d e n s i t y f u n c t i o n , w h i c h is the F o u r i e r t r a n s f o r m of the correlation f u n c t i o n
J(w)= l I C ( t ) e - i u td t = 2 Re
Lm
C(t)e-iwt d t
(4)
If a molecule u n d e r g o e s isotropic t u m b l i n g , the spectral d e n s i t y f u n c t i o n c a n be d e s c r i b e d b y a single correlation time.
(5)
Macromolecules, Vol. 19, No. 4, 1986
Polymer Dynamics-Solubility Parameters Relationship 1015
Polymer dynamics, however, is usually too complicated to be assigned to an isotropic motion. Thus a number of dynamic models have been developed. Of many available models the diamond-lattice conformation jump is most realistic. Details of the autocorrelation function and spectral density for this model will now be discussed briefly. Diamond-Lattice Model. The autocorrelation function for the VJGM model is given by16-18,21-23
J(o)= :JmC(t)e-'.'
2
dt =
-m
+ Two correlation times Td and T~ are required for description of this model. Td characterizes the three-bond conformation jump in an ideal diamond lattice, and T~ reflects the long-range tumbling. erfc is the complementary error function. The spectral density corresponding to eq 6 is22123 J(o)= TOTd(T0
(70
-
Td)'
- Td)
+
((:)'"[
W2T2Td2
( 2 )=[ li2 WToTd
+
(1
(1
+
+
W2T02)12
1 W2T02)1i2
1
+
-
LJ
+
+1
+ W2T02
-1 -
W2T02
]li2
1I) (7)
Polymer Diamond-Lattice Conformation Jump with Side-Chain Internal Rotation. The VJGM model There are four parameters in our model. Td and T~ are was successfully applied to polymer main-chain motion,21-23 correlation times of backbone motion characterized as in but it cannot be applied to describe PBMA motion in eq 6. S2and T , are the parameters for side-chain internal concentrated solution since both main-chain diffusion and rotation with physical meaning the same as in eq 8. If side-chain internal rotation should be considered for this there is no side-chain motion in the polymer, then S2 = complicated polymer system. We thus modified the 1, eq 10 is reduced to eq 7, and the VJGM model is reVJGM model by superimposing side-chain internal rotacovered. tion on main-chain motion. We adopted the "model-free" To extract dynamic information about side-chain motcorrelation function of internal rotation of a polymer side chain, which has been described by Szabo and L i ~ a r i . ~ ~ion, the first step is to evaluate the dynamic parameters Td and T~ for main-chain motion. For a nucleus in the macromolecular backbone, s2= 1,the values Td and T~ can Ci(t) = S 2 (1- S2)e-t/Te i8) be determined by a nonlinear optimization from multinuclear relaxation experimental data (Tl and NOE values). where S2 (0 I S25 1) is the degree of spatial restriction After Td and T~ are fixed, S2and T , are obtained by the of the internal rotation and T , is an effective correlation same program from side-chain carbon T,s and NOES. time. If S2 = 0, then the internal motion is similar to isotropic. On the other hand, if S2= 1,then the internal Results and Discussion motion is completely restricted (rigid). The T1 values of PBMA in three dispersed magnetic The correlation function for conformational jumps of fields and in nine selected solvents that have quite varied polymer main chains with internal rotation of side chains solubility for PBMA are listed in Table I. This reveals can be written as the product of correlation functions for a few interesting trends. The Tls for the main-chain the main-chain motion and that for internal motion, procarbons C-CH2 generally increase with the strength of vided that the two motions can be considered independent magnetic field. This is expected since our measurements and uncorrelated.24-26If the overall motion is not isotropic, were performed in concentrated solutions near room temthe total correlation function cannot be rigorously factored perature (45 "C), where the main-chain motion should be into a produce of correlation functions of overall and inquite slow (outside of extreme narrowing). One interesting ternal motions. Nevertheless, Szabo et al.24have shown fact that has been observed previously is that the Tls for with convincing evidence that this decoupling approxiall side-chain carbons including the methyl groups also mation is valid for the model of overall anisotropic motion show a consistently large field dependence. Simple theoof a main chain with internal rotation of side chain even ry27728predicts that the dipolar T, of a carbon is indein cases where a distribution of correlation times has been pendent of the magnetic field strength if the correlation involved (e.g., for random-coil polymers). We approximate time is within the extreme narrowing region. the total correlation function as a product of the diaA few papers have discussed the solvent dependence of mond-lattice correlation function and internal rotation Tl values on polymer main chains.2B11Generally, in dilute C(t) = [e-ltl/ro + Itl/Td][erfc(lt1/Td)"2][S2 + (1- S2)e+e] solution (C50 mg/mL) polymer main chains have higher T, values in good solvents and lower T , values in poor (9) solvents. Our experiment shows that this observation is The nuclear spin relaxation parameters are expressed in not seen for concentrated polymer solutions (where W ~ T ; terms of the spectral density. presumably will always exceed 1at current magnetic fields,
+
1016 Levy and Wang
Macromolecules, L'oL 19, N o . 1, 1986
Table I1 NOEF of Poly(n-butyl methacrylate) Carbons in Different Solvents (476 mg/mL) and Different Magnetic Fields at 45 "C KOEF solvent S ,(caI,'cm3)' C-1 c-2 c-3 C-4 C-CH3 C-CH2 C-CR, 90.6 hlHz 1.9 1.6 I .9 0.94 0.44 0.72 toluene 0.15 0.97 1.7 0.66 0.54 0.63 1.4 1.6 0.35 0.83 tetrahydrofuran 1.7 1.0 0.39 0.61 1.4 1.6 chlorobenzene 0.75 0.74 1.%5 1.4 1.7 0.89 0.47 0.84 1,1
